Finite Group Databasebeta

← #15760339

Subgroups — #15760339

Order 3328.

450 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13120048C211yesmaximal, characteristic
2#13114832C211yesmaximal, characteristic
3#13113520C212yesmaximal
4#13112738C212yesmaximal
5C13×#2983C211yesmaximal, characteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C2×#88123C2211yescharacteristic
8C13×#446—24no—
9C13×#432—22no—
10C13×#431C2212yes—
11#11718891—21no—
12C2×#88076—21no—
13#11718647C414yes—
14#11718638—21no—
15C4×C4⋊Dic13C2211yescharacteristic
16#11718590—22no—
17#11718585C2212yes—
18#11718122—21no—
19#11718074—24no—
20C22×Q8×C13D411yescharacteristic
21C22×Dic26—21no—
22C4×Q8×C13—22no—
23C4×Q8×C13—22no—
24C2×C13×C4⋊C4C2×C412yes—
25C2×C13×C4⋊C4D411yescharacteristic
26C2×C42×C13D412yes—
27C2×C42×C13C2311yescharacteristic
28C2×C4⋊Dic13—21no—
29C2×C4⋊Dic13—21no—
30C2×C4⋊Dic13C2×C412yes—
31C2×C4×Dic13—21no—
32C2×#6099—22no—
33#88123—22no—
34#88123—22no—
35C13×C4⋊C8—24no—
36C13×C4⋊C8D414yes—
37C13×C22⋊C8—22no—
38C13×#97—24no—
39C4×C8×C13—22no—
40#88076—42no—
41#88071—24no—
42#88071—24no—
43#88071C2×C412yes—
44C4⋊#1055—22no—
45C4⋊#1055—22no—
46#9404—131nomaximal, Sylow
47C2×Q8×C13—22no—
48C2×Q8×C13—21no—
49C2×Q8×C13—21no—
50C2×Q8×C13—22no—
51C22×C4×C13C22⋊C412yes—
52C22×C4×C13C22⋊C412yes—
53C22×C4×C13C22×C411yescharacteristic
54C22×C4×C13C2×D411yescharacteristic
55C22×C4×C13C2×D411yescharacteristic
56C22×Dic13—22no—
57C22×Dic13—22no—
58C2×Dic26—44no—
59C2×Dic26—41no—
60C2×Dic26—41no—
61C2×C8×C13—24no—
62C13×C4⋊C4—24no—
63C13×C4⋊C4—22no—
64C42×C13—22no—
65C42×C13—22no—
66C42×C13C2×D412yes—
67C42×C13#4112yes—
68C4⋊Dic13—24no—
69C4⋊Dic13—42no—
70C4⋊Dic13—42no—
71C4×Dic13—41no—
72C4×Dic13—41no—
73#6099—42no—
74#6099—42no—
75C2×#1055—42no—
76#2983D1311yescharacteristic
77#2568—131no—
78#1801—131no—
79#1549—132no—
80#1303—132no—
81C23×C13C2×C22⋊C411yescharacteristic
82Q8×C13—42no—
83Q8×C13—42no—
84C2×C4×C13—22no—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13—41no—
90C2×C4×C13—42no—
91C2×C4×C13C4×D412yes—
92C2×C4×C13#12011yescharacteristic
93C2×C4×C13#12112yes—
94C2×C4×C13#12311yescharacteristic
95C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
96C2×C4×C13#13712yes—
97C2×C4×C13#13711yescharacteristic
98C2×Dic13—42no—
99C2×Dic13—44no—
100C2×Dic13—42no—
101C2×Dic13—42no—
102C2×Dic13—42no—
103Dic26—82no—
104Dic26—82no—
105C8×C13—44no—
106#1055—82no—
107C2×C4⋊Q8—131no—
108C2×C4×Q8C2×D1311yescharacteristic
109#446—24no—
110#432—22no—
111#431C2×D1312yes—
112#423—132no—
113C2×#101—261no—
114#400—134no—
115#391—261no—
116#391—262no—
117#382—261no—
118C4×C4⋊C4—131no—
119#343—261no—
120#332—264no—
121C22×C13—21no—
122C22×C13—21no—
123C22×C13#38611yescharacteristic
124C22×C13#41711yescharacteristic
125C22×C13#41911yescharacteristic
126C4×C13—21no—
127C4×C13—22no—
128C4×C13—42no—
129C4×C13—42no—
130C4×C13#45412yes—
131C4×C13#46812yes—
132C4×C13#47012yes—
133Dic13—82no—
134Dic13—82no—
135C22×Q8—261no—
136C22×Q8D5211yescharacteristic
137C2×M16—262no—
138C4⋊Q8—262no—
139C4⋊Q8—262no—
140C4×Q8—22no—
141C4×Q8—22no—
142C2×C4⋊C4—132no—
143C2×C4⋊C4—261no—
144C2×C4⋊C4—261no—
145C2×C4⋊C4C4×D1312yes—
146C2×C4⋊C4D5211yescharacteristic
147C2×C42—261no—
148C2×C42C22⋊D1312yes—
149C2×C42C22×D1311yescharacteristic
150C4⋊C8—24no—
151C4⋊C8—262no—
152C4⋊C8—262no—
153C4⋊C8C22⋊D1314yes—
154#101—522no—
155C22⋊C8—22no—
156#97—24no—
157C4×C8—22no—
158#95—132no—
159#95—264no—
160#95—264no—
161C2×C13—21no—
162C2×C13—21no—
163C2×C13#188811yescharacteristic
164C2×C13#189411yescharacteristic
165C2×C13#191511yescharacteristic
166C2×Q8—21no—
167C2×Q8—22no—
168C2×Q8—21no—
169C2×Q8—22no—
170C2×Q8—524no—
171C2×Q8—521no—
172C2×Q8—521no—
173C22×C4—262no—
174C22×C4—262no—
175C22×C4#610312yes—
176C22×C4#610312yes—
177C22×C4C2×C4×D1311yescharacteristic
178C22×C4C2×D5211yescharacteristic
179C22×C4C2×C22⋊D1311yescharacteristic
180M16—522no—
181M16—522no—
182C2×C8—24no—
183C2×C8—522no—
184C4⋊C4—24no—
185C4⋊C4—22no—
186C4⋊C4—264no—
187C4⋊C4—522no—
188C4⋊C4—522no—
189C42—22no—
190C42—22no—
191C42—521no—
192C42—521no—
193C42#612712yes—
194C42C2×C22⋊D1312yes—
195C13#940411yescharacteristic, complemented, Sylow
196C23C2×#610311yescharacteristic
197Q8—42no—
198Q8—42no—
199Q8—1042no—
200Q8—1042no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—41no—
207C2×C4—42no—
208C2×C4—522no—
209C2×C4—522no—
210C2×C4—524no—
211C2×C4—522no—
212C2×C4—522no—
213C2×C4#8816211yescharacteristic
214C2×C4#8816312yes—
215C2×C4#8816311yescharacteristic
216C2×C4C4×C22⋊D1312yes—
217C2×C4#8818311yescharacteristic
218C2×C4#8818412yes—
219C2×C4#8820711yescharacteristic
220C8—44no—
221C8—1042no—
222C22—21no—
223C22—21no—
224C22#1171878111yescharacteristic
225C22#1171879411yescharacteristic
226C22#1171887411yescharacteristic
227C4—21no—
228C4—22no—
229C4—42no—
230C4—42no—
231C4—1042no—
232C4—1042no—
233C4#1171879512yes—
234C4#1171879812yes—
235C4#1171890612yes—
236C2—21no—
237C2—21no—
238C2#1311523911yescharacteristic
239C2#1311526911yescharacteristic
240C2#1311538811yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2983C2
socleC22×C13#386
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2983D13
hypocenterC13#9404
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
195. C13#9404semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#131200482
#131148322
#131135202
#131127382
C13×#29832
#940413